Approximately gaussian marginals and the hyperplane conjecture
Metric Geometry
2010-01-07 v1
Abstract
We discuss connections between certain well-known open problems related to the uniform measure on a high-dimensional convex body. In particular, we show that the "thin shell conjecture" implies the "hyperplane conjecture". This extends a result by K. Ball, according to which the stronger "spectral gap conjecture" implies the "hyperplane conjecture".
Cite
@article{arxiv.1001.0875,
title = {Approximately gaussian marginals and the hyperplane conjecture},
author = {Ronen Eldan and Bo'az Klartag},
journal= {arXiv preprint arXiv:1001.0875},
year = {2010}
}